Doppler-sensitive adaptive coherence estimate detector methods

ABSTRACT

A method is provided for detecting a target signal of a specific known form in the presence of clutter. The method includes dividing a set of initial training data, derived from returns from a burst of identical pulses, into a set of censored data and a set of uncensored data. A covariance matrix estimate, based on the uncensored data, is used to compute adaptive coherence estimate values, and an average adaptive coherence estimate threshold level is computed for each Doppler band to obtain a corresponding threshold. The censored data and the covariance matrix estimate are used to compute adaptive coherence estimate values for the uncensored data for each Doppler band, and these values are compared with the respective thresholds to determine the presence or absence of the target signal.

FIELD OF THE INVENTION

The present invention generally relates to adaptive coherence estimatedetectors, particularly for, but not limited to, airborne radarapplications.

BACKGROUND OF THE INVENTION

In applications such as radar, sonar, data communications, time seriesanalysis, and array processing, an object is to determine whether aspecific signal is present in a series of N measured data samples (whichcan be represented as Z=[z(0), z(1), . . . , z(N−1)]^(r)) that containunknown interference and noise. Based on these data samples, a decisionmust be made between two possible hypotheses, viz., the null hypothesisH₀ in which the data consists of interference only, and the alternatehypothesis H₁ in which the signal is present in the data as well. Thesetwo hypotheses are exemplified via the mathematical representation ofthe measured data samples:z=αs+n  (1)where s is the signal vector, with α is its associated complexamplitude, and n is the noise plus interference. Under hypothesis H₀,the signal amplitude is α=0, whereas under hypothesis H₁, the signalamplitude is α≠0. The covariance of the noise plus interference is R,which is employed in Matched Subspace Detectors (MSDs) to effectivelysuppress the noise and interference to enable reliable detectionperformance (as a function of the signal-to-noise ratio (SNR) and theseparability of the signal and interference). (See, for example, L. L.Scharf and B. Friedlander, “Matched subspace detectors,” IEEE Trans.Signal Processing, Vol. 42, No. 8, pp. 2146–2157, August 1994.) Inpractice, however, R is not known and must, therefore, be estimated.Hence, the detector performance is also highly dependent upon theaccuracy of the covariance matrix estimate {tilde over (R)}. MSDs thatuse the estimated covariance matrix are known as Adaptive SubspaceDetectors (ASDs) because they adapt to the measured data.

An Adaptive Coherence Estimate (ACE) detector, which is also known as anAdaptive Cosine Detector, is one such ASD in which the specific form ofthe desired signal is known (as opposed to detectors that test for thepresence of any signal that lies within the signal subspace), but thepower level of the noise and interference is unknown (see, e.g., L. L.Scharf and L. T. McWhorter, “Adaptive matched subspace detectors andadaptive coherence estimators,” Proc. 30^(th) Asilomar Conf. on Signals,Systems, and Computers, Vol. 1, pp. 1114–1117, Nov. 3–6, 1996; L. T.McWhorter, L. L. Scharf, and L. J. Griffiths, “Adaptive coherenceestimation for radar signal processing,” Proc. 30^(th) Asilomar Conf. onSignals, Systems, and Computers, Vol. 1, pp. 536–540, Nov. 3–6, 1996;and S. Kraut, L. L. Scharf, and L. T. McWhorter, “Adaptive subspacedetectors,” IEEE Trans. Signal Processing, Vol. 49, No. 1, January2001]). For each range index k the ACE takes the form

$\begin{matrix}{{{ACE}(k)} = \frac{{{s^{H}{\overset{\sim}{R}}^{- 1}z_{k}}}^{2}}{\left( {s^{H}{\overset{\sim}{R}}^{- 1}s} \right)\left( {z_{k}^{H}{\overset{\sim}{R}}^{- 1}z_{k}} \right)}} & (2)\end{matrix}$wherein s, R and z are as defined above, and H denotes the Hermitianmatrix or complex conjugate transpose. The resulting ACE value for agiven data vector z_(k) is then compared with a predetermined thresholdto achieve a desired probability of false alarm. The ACE is boundedbetween 0 and 1 and effectively determines a measure of coherence of thecell-under-test (CUT) with the desired steering vector (that models atarget return signal from the corresponding spatial direction andDoppler frequency).

SUMMARY OF THE INVENTION

Generally speaking, one aspect of the present invention concerns amethod for selecting the threshold for the ACE detector, and, moreparticularly, in preferred embodiments, selecting the threshold forairborne radar applications in which a form of censored Space-TimeAdaptive Processing (STAP) is employed. An important feature ofpreferred embodiments of the invention is that the coherent nature ofthe ACE test statistic thereby enables an appropriate threshold to beset for each individual Doppler frequency band, hence resulting insubstantially improved target signal detection performance as comparedwith a conventional “uniform threshold across” Doppler system.

In accordance with one aspect of the invention, there is provided amethod for selecting a threshold for an adaptive coherence estimatedetector for an airborne radar application and detecting a target signalusing the threshold wherein a specific form of a target signal to bedetected is known, said method comprising the steps of:

determining a Doppler frequency for a clutter ridge of a clutter returnfrom ground of a radar beam transmitted from an airborne radar antenna;

determining the proximity of a Doppler band of interest to the Dopplerfrequency of clutter ridge; and

setting the threshold of the adaptive coherence estimate detector basedon the proximity of the Doppler band of interest to the clutter ridge.

Preferably, target detection is based on returns from a burst of Midentical pulses transmitted over N radio frequency channels,

input data in the respective channels are sampled to form range cellsamples for each pulse,

snapshots are formed by stacking, in succession, N-length data vectorsassociated with each of the channels for each of the M pulses,

signal presence is sought in one range cell at a time,

the snapshots are censored so as to divide a set of K initial trainingdata into (i) a set of K_(c) censored training data snapshots that maypotentially contain a target, and (ii) a set of K_(u) uncensoredtraining data snapshots,

a covariance estimate is computed based on the uncensored snapshots,

the covariance estimate is used in computing an adaptive coherenceestimate values for the K_(c) censored snapshots for each of the MDoppler frequency bands and in computing a quiescent adaptive coherenceestimate threshold level for the K_(u) uncensored snapshots for each ofthe M Doppler frequency bands,

threshold levels so computed are averaged over the uncensored rangecells to yield a M-length threshold vector wherein each vector elementcorresponds to the quiescent estimate level for a particular Doppler,and

the adaptive coherence estimate values for the K_(c) censored snapshotsare compared with a corresponding quiescent estimate level to detect thepresence or absence of a target signal.

Preferably, the covariance matrix estimate comprised of only the K_(u)uncensored snapshots, denoted {tilde over (R)}_(c), is used to computethe adaptive coherence estimate values, denoted ACE_(CTD)(m,k_(c)), forthe set of k_(c)=1, 2 . . . K_(c) censored training data snapshots,denoted z_(CTD,k) _(c) , for each of the m=1, 2, . . . , M Dopplerfrequency bands, using a steering vector s_(m) in accordance with theequation:

ACE CTD ⁡ ( m , k c ) =  s m H ⁢ R ~ c - 1 ⁢ z CTD , k c  2 ( s m H ⁢ R ~c - 1 ⁢ m ) ⁢ ( z CTD , k c H ⁢ R ~ c - 1 ⁢ z CTD , k c )wherein H denotes the Hermitian matrix and s_(m), {tilde over (R)}_(c),and Z_(CTD,k) _(c) are defined as above

Preferably, the covariance matrix estimate, denoted {tilde over(R)}_(c), is used to compute the adaptive coherence estimate levels,denoted ACE_(UTD)(m,k_(u)), for the set of k_(u)=1, 2 . . . K_(u)uncensored training data snapshots, denoted z_(UTD,k) _(u) , for each ofthe m=1, 2, . . . , M Doppler frequency bands, using a steering vectors_(m) in accordance with the equation:

ACE UTD ⁡ ( m , k u ) =  s m H ⁢ R ~ c - 1 ⁢ z UTD , k u  2 ( s m H ⁢ R ~c - 1 ⁢ ⁢ ⁢ m ) ⁢ ( z UTD , k u H ⁢ R ~ c - 1 ⁢ z UTD , k u )wherein H denotes the Hermitian matrix, and z_(UTD,k) _(u) , s_(m) and{tilde over (R)}_(c) are defined as above.

Preferably, the M-length threshold vector, denoted γ, is computed usingthe equation:

$\gamma = {\begin{bmatrix}{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {1,k_{u}} \right)}}} \\M \\{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {M,k_{u}} \right)}}}\end{bmatrix}.}$

Advantageously, the quiescent adaptive coherence estimate thresholdlevel is scaled to obtain a desired level of false alarms. The thresholdis preferably scaled using a minimum desired threshold level.Advantageously, scaled threshold, denoted τ_(m), for the m^(th) Dopplerband is scaled asτ_(m)=max(βγ_(m),τ_(min))wherein β is a scale factor used to set a desired probability of falsealarm which is constant over m=1, 2, . . . , M, γ_(m) is the value ofthe threshold for the m^(th) Doppler, and τ_(min) is a minimum desiredthreshold level.

According to a further aspect of the invention, there is provided amethod for detecting a signal of a specific known form in the presenceof clutter, said method comprising:

dividing a set of initial training data derived from returns from aburst of identical pulses, into a set of censored data and a set ofuncensored data;

using the uncensored data to compute a covariance matrix estimate;

using the covariance matrix estimate to compute adaptive coherenceestimate values;

computing an average adaptive coherence estimate threshold for eachDoppler band so as to obtain a threshold;

using the censored data of step (i) and the covariance matrix estimateof step (ii) to compute adaptive coherence estimate values for theuncensored data for each Doppler band; and

comparing the adaptive coherence estimate values computed in step (v)with the respective thresholds computed in step (iv) to determine thepresence or absence of the signal of a specific known form.

Preferably, as discussed above, the covariance matrix estimate, denoted{tilde over (R)}_(c), is used to compute the adaptive coherence estimatevalues, denoted ACE_(CTD)(m,k_(c)), for the set of k_(c)=1, 2 . . .K_(c) censored training data snapshots, denoted Z_(CTD,k) _(c) , foreach of the m=1, 2, . . . , M Doppler frequency bands, using a steeringvector s_(m) in accordance with the equation:

ACE CTD ⁡ ( m , k c ) =  s m H ⁢ R ~ c - 1 ⁢ z CTD , k c  2 ( s m H ⁢ R ~c - 1 ⁢ m ) ⁢ ( z CTD , k c H ⁢ R ~ c - 1 ⁢ z CTD , k c ) .wherein H denotes the Hermitian matrix and s_(m), {tilde over (R)}_(c),and z_(CTD,k) _(c) are defined as above.

As was also discussed above, preferably, the covariance matrix estimate,denoted {tilde over (R)}_(c), is used to compute the adaptive coherenceestimate levels, denoted ACE_(UTD)(m,k_(u)), for the set of k_(u)=1, 2 .. . K_(u) uncensored training data snapshots, denoted z_(UTD,k) _(u) ,for each of the m=1, 2, . . . , M Doppler frequency bands, using asteering vector s_(m) in accordance with the equation:

ACE UTD ⁡ ( m , k u ) =  s m H ⁢ R ~ c - 1 ⁢ z UTD , k u  2 ( s m H ⁢ R ~c - 1 ⁢ m ) ⁢ ( z UTD , k u H ⁢ R ~ c - 1 ⁢ z UTD , k u ) .wherein H denotes the Hermitian matrix, and z_(UTD,k) _(u) , s_(m) and{tilde over (R)}_(c) are defined as above.

Preferably, the M-length threshold vector, denoted γ, is, computed usingthe equation:

$\gamma = {\begin{bmatrix}{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {1,k_{u}} \right)}}} \\M \\{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {M,k_{u}} \right)}}}\end{bmatrix}.}$

As discussed above, advantageously, the quiescent adaptive coherenceestimate threshold level is scaled to obtain a desired level of falsealarms. The threshold is preferably scaled using a minimum desiredthreshold level. Preferably, the scaled threshold, denoted τ_(m), forthe m^(th) Doppler band is scaled asτ_(m)=max(βγ_(m),τ_(min))wherein β is a scale factor used to set a desired probability of falsealarm which is constant over m=1, 2, . . . , M, γ_(m) is the value ofthe threshold for the m^(th) Doppler, and τ_(min) is a minimum desiredthreshold level.

In accordance with yet another aspect of the invention, there isprovided a method for selecting a threshold for an adaptive coherenceestimate detector and detecting a target signal using the thresholdwherein a specific form of a target signal to be detected is known, saidmethod comprising the steps of:

receiving returns from a burst of M identical pulses transmitted over Nradio frequency channels,

sampling input data in the respective channels to form range cellsamples for each pulse,

forming snapshots by stacking, in succession, N-length data vectorsassociated with each of the channels for each of the M pulses,

censoring the snapshots so as to divide a set of K initial training datainto (i) a set of K^(c) censored training data snapshots that maypotentially contain a target, and (ii) a set of K^(u) uncensoredtraining data snapshots,

computing a covariance estimate based on the uncensored snapshots,

using the covariance estimate in computing an adaptive coherenceestimate values for the K^(c) censored snapshots for each of the MDoppler frequency bands and in computing a quiescent adaptive coherenceestimate threshold level for the K^(u) uncensored snapshots for each ofthe M Doppler frequency bands,

averaging the threshold levels so computed over the range cellscorresponding to the uncensored snapshots to yield a M-length thresholdvector wherein each vector element corresponds to the quiescent adaptivecovariance estimate level for a particular Doppler; and

comparing the adaptive coherence estimate values for the K_(c) censoredsnapshots with corresponding adaptive coherence estimate quiescentlevels to detect the presence or absence of the target signal.

Preferably, as discussed hereinabove, the covariance matrix estimate,denoted {tilde over (R)}_(c), is used to compute the adaptive coherenceestimate values, denoted ACE_(CTD)(m,k_(c)), for the set of k_(c)=1, 2 .. . K_(c) censored training data snapshots, denoted z_(CTD,k) _(c) , foreach of the m=1, 2, . . . , M Doppler frequency bands, using a steeringvector s_(m) in accordance with the equation:

ACE CTD ⁡ ( m , k c ) =  s m H ⁢ R ~ c - 1 ⁢ z CTD , k c  2 ( s m H ⁢ R ~c - 1 ⁢ m ) ⁢ ( z CTD , k c H ⁢ R ~ c - 1 ⁢ z CTD , k c ) .wherein H denotes the Hermitian matrix and s_(m), {tilde over (R)}_(c),and z_(CTD,k) _(c) are defined as above.

Again, preferably, the covariance matrix estimate, denoted {tilde over(R)}_(c), is used to compute the adaptive coherence estimate levels,denoted ACE_(UTD)(m,k_(u)), for the set of k_(u)=1, 2 . . . K_(u)uncensored training data snapshots, denoted z_(UTD,k) _(u) , for each ofthe m=1, 2, . . . , M Doppler frequency bands, using a steering vectors_(m) in accordance with the equation:

ACE UTD ⁡ ( m , k u ) =  s m H ⁢ R ~ c - 1 ⁢ z UTD , k u  2 ( s m H ⁢ R ~c - 1 ⁢ m ) ⁢ ( z UTD , k u H ⁢ R ~ c - 1 ⁢ z UTD , k u ) .wherein H denotes the Hermitian matrix, and Z_(UTD,k) _(u) , s_(m) and{tilde over (R)}_(c) are defined as above.

Preferably, as discussed hereinbefore, the M-length threshold vector, γ,is computed using the equation:

$\gamma = {\begin{bmatrix}{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {1,k_{u}} \right)}}} \\M \\{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {M,k_{u}} \right)}}}\end{bmatrix}.}$

Again, the quiescent adaptive coherence estimate threshold level ispreferably scaled to obtain a desired level of false alarms, thethreshold is preferably scaled using a minimum desired threshold level,and most preferably, the scaled threshold, denoted τ_(m), for the m^(th)Doppler band is scaled asτ_(m)=max(βγ_(m),τ_(min))wherein β is a scale factor used to set a desired probability of falsealarm which is constant over m=1, 2, . . . , M, γ_(m) is the value ofthe threshold for the m^(th) Doppler, and τ_(min) is a minimum desiredthreshold level.

Further features and advantages of the present invention will be setforth in, or apparent from, the detailed description of preferredembodiments thereof which follows.

BRIEF DESCRIPTION OF THE DRAWINGS

The single FIGURE in the drawings is a flow chart or block diagram ofthe basic steps employed in a detection method in accordance with apreferred embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Considering some additional-background in connection with embodimentsdirected to radar applications, the Pulse Repetition Frequency (PRF) ofthe radar pulse scan determines the bandwidth of the Doppler frequencyspectrum. The Doppler spectrum is partitioned into M frequency bands(for M consecutive pulses) in which targets are sought at eachindividual range gate of the radar platform by using the steering vectors_(m) associated with the m^(th) Doppler frequency band. For airborneradar performing Ground Moving Target Indication (GMTI), the returnsfrom the ground, also know as clutter returns, are a major source ofinterference. For an antenna array beam focused at a particular azimuthangle and depression angle with respect to the motion of the radarplatform, the clutter returns are received at a prescribed Dopplerfrequency which can be approximately calculated given the radaroperating parameters.

The power level of the clutter return dictates to a large degree thethreshold level for the ACE detector, according to the proximity to theclutter Doppler of a Doppler frequency band of interest. This can beillustrated by assuming the clutter return is comprised of a singleDoppler frequency such that the measured data vector at a range cellthat does contain a target can be modeled as z_(c)=αs_(c), where s_(c)is the steering vector of the clutter and α is a scaling factor(assuming for the sake of simplicity that the clutter is not spread inDoppler as actually occurs in practice). If the ACE value is thencomputed at the Doppler frequency associated with s_(c), it is notdifficult to show that equation (2) above will result in an ACE valuethat is identically 1. One aspect of the present invention provides forsetting the ACE threshold higher according to the proximity to theclutter ridge of a Doppler band of interest. In other words, the closerthe clutter ridge to the Doppler band of interest, the higher the ACEthreshold should be set. As discussed below, a further aspect of theinvention concerns also setting a minimum for the ACE threshold so thatthe ACE threshold for Doppler bands further away from the clutter ridgeis not less than a predetermined minimum.

In order to provide a better understanding of the invention, consider aradar system that consists of an N-element antenna array which providesN Radio Frequency (RF) antenna channels. Time-delayed inputs of the Nchannels are to be combined via linear weighting to form an output suchthat an output performance measure (such as signal-to-noise (SNR) powerratio) is optimized. Assume that for each of these RF channels, theradar front end carries out amplification, filtering, reduction tobaseband, and analog-to-digital (A/D) conversion. The output of each A/Dis a data stream of in-phase and quadrature-phase (I, Q) output pairs.The I and Q components represent the real and imaginary parts,respectively, of the complex valued data stream.

The radar waveform is assumed to be a burst of M identical pulses withpulse repetition interval (PRI) equal to T. Target detection is basedupon the returns from this burst. The input data in the respectivechannels are sampled to form range-gate samples for each pulse. For thek^(th) range gate, an MN-length sample vector z_(k) is formed. Inparticular, this vector, which is called a snapshot, is formed bystacking, in succession, the N-length data vectors associated with eachof the antenna channels for each of the M pulses. Signal presence issought in one range gate at a time and, as indicated above, theparticular range gate at which signal presence is sought is called thecell-under-test (CUT).

In accordance with an important feature of preferred embodiments of theinvention, the local snapshots (in terms of range) that may potentiallycontain a target are censored such that the set of K initial trainingdata (ITD) snapshots are separated into a set of K_(c) censored trainingdata (CTD) snapshots and a set of K_(u) uncensored training data (UTD)snapshots. More generally, the data are split into two kinds of trainingdata, censored and uncensored. In preferred embodiments, this is doneusing APR (Adaptive Power Residue) techniques wherein targets are soughtthat match a particular space-time training vector, or GIP whichessentially involves looking for statistical outliers. Both of thesetechniques are conventional.

As a consequence of splitting the data as described above, twocovariance matrix estimates can be computed, viz., {tilde over (R)}_(u),the ITD covariance matrix estimate comprised of both censored anduncensored local snapshots, and {tilde over (R)}_(c), the UTD covariancematrix estimate comprised of only the uncensored local snapshots. Inpreferred embodiments of the invention, only the UTD covariance matrixestimate {tilde over (R)}_(c) is used. Specifically, the UTD covariancematrix estimate {tilde over (R)}_(c) is employed in equation (2) aboveto compute the ACE values for the block of k_(c)=1, 2, . . . , K_(c)local censored snapshots z_(CTD,k) _(c) for each of the m=1, 2, . . . ,M Doppler frequency bands using the associated steering vector s_(m)using the equation

ACE CTD ⁡ ( m , k c ) =  s m H ⁢ R ~ c - 1 ⁢ z CTD , k c  2 ( s m H ⁢ R ~c - 1 ⁢ m ) ⁢ ( z CTD , k c H ⁢ R ~ c - 1 ⁢ z CTD , k c ) ( 3 )wherein the various quantities are defined as discussed above. It isthis range value that is to be compared with the ACE threshold todetermine if a target exists at the particular range cell.

To determine the level of the ACE threshold, a quiescent ACE level iscomputed which corresponds to the H₀ hypothesis where no target ispresent. This is accomplished by determining the ACE values for theblock of k_(u)=1, 2, . . . , K_(u) local uncensored snapshots z_(UTD,k)_(u) for each of the m-1, 2, . . . , M Doppler frequency bands as

ACE UTD ⁡ ( m , k u ) =  s m H ⁢ R ~ c - 1 ⁢ z UTD , k u  2 ( s m H ⁢ R ~c - 1 ⁢ m ) ⁢ ( z UTD , k u H ⁢ R ~ c - 1 ⁢ z UTD , k u ) ( 4 )wherein, again, the various quantities are defined as discussed above.

More generally, equation (4), which employs the uncensored snapshots, isused to determine the level of the ACE threshold. Equation (3), whichemploys the censored snapshots, is used to derive the range value to becompared with the ACE threshold.

It is noted that this approach is different from the way in which theCFAR test statistic is computed (see K. Gerlach and S. D. Blunt,“Efficient reiterative censoring of robust STAP using the FRACTAalgorithm,” Proc. IEEE International Radar Conference 2003 and S. D.Blunt and K. Gerlach, “Efficient robust adaptive matched filtering usingthe FRACTA algorithm: results from KASSPER I,” submitted to IEEE Trans.AES) wherein the quiescent level is determined using the ITD covariancematrix {tilde over (R)}_(u) so that target Adaptive Power Residues(APRs) stand our more from the background interference.

After the computations set forth above are completed, the local UTD ACEsfor each Doppler are averaged over the uncensored range cells to yieldthe M-length threshold vector

$\begin{matrix}{\gamma = \begin{bmatrix}{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {1,k_{u)}} \right.}}} \\{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {M,k_{u}} \right.}}}\end{bmatrix}} & (5)\end{matrix}$in which each element of the vector corresponds to the quiescent ACE fora particular Doppler frequency band and will lie between 0 and 1.

In order to obtain the desired level of false alarm, the ACE thresholdfor the m^(th) Doppler is scaled asτ_(m)=max(βγ_(m),τ_(min))  (6)where β is a scale factor to set the desired probability of false alarmwhich is constant over m=1, 2, . . . , M, γ_(m) is the m^(th) term of γand τ_(min) is the minimum desired threshold level. As indicated above,although the ACE threshold should be set at a high level near theclutter ridge or peak, it is desirable that the threshold not be set toolow, and thus the ACE threshold is scaled as set forth in equation (6)so as to not fall below τ_(min), which, as noted above, is the minimumvalue of the threshold.

The foregoing may perhaps be better understood by referring to thesingle FIGURE of the drawings which is a flow chart or block diagram ofa preferred embodiment of the invention, and is used to summarize thesteps of the method described above. As shown, in a first, censoringstep 10, the training data z., z₂, . . . , z_(k) is divided or splitinto uncensored data and censored data, as described above.

As indicated by step or block 12 at the right in the drawings, theuncensored data is used to compute {tilde over (R)}_(c), the UTDcovariance matrix-estimate which, as shown by step or block 14, is, inturn, used to compute ACE_(UTD)(m,k), wherein there are m=1, . . . MDoppler bands or bins, and there are k=1, . . . , K range cells. This isdone using equation (4) above, in the manner described hereinbefore.

As shown by step or block 16, the result or output of step 14 is used tocompute the average ACE_(UTD)(m,k) for each Doppler to obtain thethreshold τ_(m), with a minimum threshold value greater or equal toτ_(min). This involves the use of equations (5) and (6) above.

In a parallel step or process indicated at 18, the computed value for{tilde over (R)}_(c) produced by step 12 is used together with censoreddata produced by step 10 to compute the adaptive coherence estimatevalues for the censored local snapshots k_(c)=1, 2 . . . K_(c) for eachof the Doppler frequency bands or bins m=1, 2, . . . , M, i.e., tocompute ACE_(CTD)(m,k), using equation (3) above.

Finally, as shown by step or block 20, the results of step 18, i.e., theACE_(CTD)(m,k) values, are compared with the respective thresholds τ_(m)to detect for the presence of targets, i.e., to determine whether anytargets are present based on whether the ACE_(CTD) value exceeds thecorresponding τ_(m).

This overall method is referred to herein for shorthand purposes as theDoppler Sensitive-ACE (DS-ACE). An important advantage of DS-ACEthresholding is that targets at Doppler frequencies outside of theclutter spectrum are more easily detectable than with uniformthresholding of the ACE in Doppler. Furthermore, unlike uniformthresholding, DS-ACE is a straightforward automatic technique. The useof censored and uncensored training data sets produces more accuratecovariance and resulting quiescent level estimations than does standardSTAP which performs no censoring of the data. This has been verifiedusing a validated high-fidelity clutter model wherein the automaticDS-ACE threshold method of the invention was found to detect nearlydouble the number of targets detected by uniform ACE thresholding thatis set using trial-and-error techniques.

Although the invention has been described above in relation to preferredembodiments thereof, it will be understood by those skilled in the artthat variations and modifications can be effected in these preferredembodiments without departing from, the scope and spirit of theinvention.

1. A method for selecting a threshold for an adaptive coherence estimatedetector for an airborne radar application and detecting a target signalusing the threshold wherein a specific form of a target signal to bedetected is known, said method comprising the steps of: determining aDoppler frequency for a clutter ridge of a clutter return from ground ofa radar beam transmitted from an airborne radar antenna; determining theproximity of a Doppler band of interest to the Doppler frequency ofclutter ridge; and setting the threshold of the adaptive coherenceestimate detector based on the proximity of the Doppler band of interestto the clutter ridge.
 2. A method according to claim 1 wherein targetdetection is based on returns from a burst of M identical pulsestransmitted over N radio frequency channels, wherein input data in therespective channels are sampled to form range cell samples for eachpulse, wherein snapshots are formed by stacking, in succession, N-lengthdata vectors associated with each of the channels for each of the Mpulses, wherein signal presence is sought in one range cell at a time,wherein the snapshots are censored so as to divide a set of K initialtraining data into (i) a set of K_(c) censored training data snapshotsthat may potentially contain a target, and (ii) a set of K_(u)uncensored training data snapshots, wherein a covariance estimate iscomputed based on the uncensored snapshots, wherein the covarianceestimate is used in computing an adaptive coherence estimate values forthe K_(c) censored snapshots for each of the M Doppler frequency bandsand in computing a quiescent adaptive coherence estimate threshold levelfor the K_(u) uncensored snapshots for each of the M Doppler frequencybands, wherein threshold levels so computed are averaged over theuncensored range cells to yield a M-length threshold vector wherein eachvector element corresponds to the quiescent estimate level for aparticular Doppler; and wherein the adaptive coherence estimate valuesfor the K_(c) censored snapshots are compared with a correspondingquiescent estimate level to detect the presence or absence of a targetsignal.
 3. A method according to claim 2 wherein the covariance matrixestimate, denoted {tilde over (R)}_(c), is used to compute the adaptivecoherence estimate values, denoted ACE_(CTD)(m,k_(c)), for the set ofk_(c)=1, 2 . . . K_(c) censored training data snapshots, denotedz_(CTD,k) _(c) , for each of the m=1, 2, . . . , M Doppler frequencybands, using a steering vector s_(m) in accordance with the equation:ACE CTD ⁡ ( m , k c ) =  s m H ⁢ R ~ c - 1 ⁢ z CTD , k c  2 ( s m H ⁢ R ~c - 1 ⁢ m ) ⁢ ( z CTD , k c H ⁢ R ~ c - 1 ⁢ z CTD , k c ) wherein H denotesthe Hermitian matrix and s_(m), {tilde over (R)}_(c), and z_(CTD,k) _(c)are defined as above.
 4. A method according to claim 2 wherein thecovariance matrix estimate, denoted {tilde over (R)}_(c), is used tocompute the adaptive coherence estimate levels, denotedACE_(UTD)(m,k_(u)), for the set of k_(u)=1, 2 . . . K_(u) uncensoredtraining data snapshots, denoted z_(UTD,k) _(u) , for each of the m=1,2, . . . , M Doppler frequency bands, using a steering vector s_(m) inaccordance with the equation: ACE UTD ⁡ ( m , k u ) =  s m H ⁢ R ~ c - 1 ⁢z UTD , k u  2 ( s m H ⁢ R ~ c - 1 ⁢ m ) ⁢ ( z UTD , k u H ⁢ R ~ c - 1 ⁢ zUTD , k u ) wherein H denotes the Hermitian matrix, and z_(UTD,k) _(u) ,s_(m) and {tilde over (R)}_(c) are defined as above.
 5. A methodaccording to claim 4 wherein said M-length threshold vector, denoted γ,is computed using the equation: $\gamma = {\begin{bmatrix}{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {1,k_{u}} \right)}}} \\M \\{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {M,k_{u}} \right)}}}\end{bmatrix}.}$
 6. A method according to claim 5 wherein the quiescentadaptive coherence estimate threshold level is scaled to obtain adesired level of false alarms.
 7. A method according to claim 6 whereinthe threshold is scaled using a minimum desired threshold level.
 8. Amethod according to claim 7 wherein the scaled threshold, denoted τ_(m),for the m^(th) Doppler band is scaled asτ_(m)=max(βγ_(m),τ_(min)) wherein β is a scale factor used to set adesired probability of false alarm which is constant over m=1, 2, . . ., M, γ_(m) is the value of the threshold for the m^(th) Doppler, andτ_(min) is a minimum desired threshold level.
 9. A method for detectinga signal of a specific known form in the presence of clutter, saidmethod comprising: (i) dividing a set of initial training data derivedfrom returns from a burst of identical pulses, into a set of censoreddata and a set of uncensored data; (ii) using the uncensored data tocompute a covariance matrix estimate; (iii) using the covariance matrixestimate to compute adaptive coherence estimate values; (iv) computingan average adaptive coherence estimate threshold for each Doppler bandso as to obtain a threshold; (v) using the censored data of step (i) andthe covariance matrix estimate of step (ii) to compute adaptivecoherence estimate values for the uncensored data for each Doppler band;and (vi) comparing the adaptive coherence estimate values computed instep (v) with the respective thresholds computed in step (iv) todetermine the presence or absence of the signal of a specific knownform.
 10. A method according to claim 9 wherein the covariance matrixestimate, denoted {tilde over (R)}_(c), is used to compute the adaptivecoherence estimate values, denoted ACE_(CTD)(m,k_(c)), for the set ofk_(c)=1, 2 . . . K_(c) censored training data snapshots, denotedz_(CTD,k) _(c) , for each of the m=1, 2, . . . , M Doppler frequencybands, using a steering vector s_(m) in accordance with the equation:ACE CTD ⁡ ( m , k c ) =  s m H ⁢ R ~ c - 1 ⁢ z CTD , k c  2 ( s m H ⁢ R ~c - 1 ⁢ m ) ⁢ ( z CTD , k c H ⁢ R ~ c - 1 ⁢ z CTD , k c ) wherein H denotesthe Hermitian matrix and s_(m), {tilde over (R)}_(c), and z_(CTD,k) _(c)are defined as above.
 11. A method according to claim 9 wherein thecovariance matrix estimate, denoted {tilde over (R)}_(c), is used tocompute the adaptive coherence estimate levels, denotedACE_(UTD)(m,k_(u)), for the set of k_(u)=1, 2 . . . K_(u) uncensoredtraining data snapshots, denoted z_(UTD,k) _(u) , for each of the m=1,2, . . . , M Doppler frequency bands, using a steering vector s_(m) inaccordance with the equation: ACE UTD ⁡ ( m , k u ) =  s m H ⁢ R ~ c - 1 ⁢z UTD , k u  2 ( s m H ⁢ R ~ c - 1 ⁢ m ) ⁢ ( z UTD , k u H ⁢ R ~ c - 1 ⁢ zUTD , k u ) wherein H denotes the Hermitian matrix, and z_(UTD,k) _(u) ,s_(m) and {tilde over (R)}_(c) are defined as above.
 12. A methodaccording to claim 11 wherein said M-length threshold vector, denoted γ,is computed using the equation: $\gamma = {\begin{bmatrix}{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {1,k_{u}} \right)}}} \\M \\{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {M,k_{u}} \right)}}}\end{bmatrix}.}$
 13. A method according to claim 12 wherein thequiescent adaptive coherence estimate threshold level is scaled toobtain a desired level of false alarms.
 14. A method according to claim13 wherein the threshold is scaled using a minimum desired thresholdlevel.
 15. A method according to claim 14 wherein the scaled threshold,denoted τ_(m), for the m^(th) Doppler band is scaled asτ_(m)=max(βγ_(m),τ_(min)) wherein β is a scale factor used to set adesired probability of false alarm which is constant over m=1, 2, . . ., M, γ_(m) is the value of the threshold for the m^(th) Doppler, andτ_(min) is a minimum desired threshold level.
 16. A method for selectinga threshold for an adaptive coherence estimate detector and detecting atarget signal using the threshold wherein a specific form of a targetsignal to be detected is known, said method comprising the steps of:receiving returns from a burst of M identical pulses transmitted over Nradio frequency channels, sampling input data in the respective channelsto form range cell samples for each pulse, forming snapshots bystacking, in succession, N-length data vectors associated with each ofthe channels for each of the M pulses, censoring the snapshots so as todivide a set of K initial training data into (i) a set of K_(c) censoredtraining data snapshots that may potentially contain a target, and (ii)a set of K_(u) uncensored training data snapshots, computing acovariance estimate based on the uncensored snapshots, using thecovariance estimate in computing an adaptive coherence estimate valuesfor the K_(c) censored snapshots for each of the M Doppler frequencybands and in computing a quiescent adaptive coherence estimate thresholdlevel for the K_(u) uncensored snapshots for each of the M Dopplerfrequency bands, averaging the threshold levels so computed over therange cells corresponding to the uncensored snapshots to yield aM-length threshold vector wherein each vector element corresponds to thequiescent adaptive coherence estimate level for a particular Doppler;and comparing the adaptive coherence estimate values for the K_(c)censored snapshots with corresponding adaptive coherence estimatequiescent levels to detect the presence or absence of the target signal.17. A method according to claim 16 wherein the covariance matrixestimate, denoted {tilde over (R)}_(c), is used to compute the adaptivecoherence estimate values, denoted ACE_(CTD)(m,k_(c)), for the set ofk_(c)=1, 2 . . . K_(c) censored training data snapshots, denotedZ_(CTD,k) _(c) , for each of the m=1, 2, . . . , M Doppler frequencybands, using a steering vector s_(m) in accordance with the equation:ACE CTD ⁡ ( m , k c ) =  s m H ⁢ R ~ c - 1 ⁢ z CTD , k c  2 ( s m H ⁢ R ~c - 1 ⁢ m ) ⁢ ( z CTD , k c H ⁢ R ~ c - 1 ⁢ z CTD , k c ) wherein H denotesthe Hermitian matrix and s_(m), {tilde over (R)}_(c), and z_(CTD,k) _(c)are defined as above.
 18. A method according to claim 16 wherein thecovariance matrix estimate, denoted {tilde over (R)}_(c) is used tocompute the adaptive coherence estimate levels, denotedACE_(UTD)(m,k_(u)), for the set of k_(u)=1, 2 . . . K_(u) uncensoredtraining data snapshots, denoted z_(UTD,k) _(u) , for each of the m=1,2, . . . , M Doppler frequency bands, using a steering vector s_(m) inaccordance with the equation:${{ACE}_{UTD}\left( {m,k_{u}} \right)} = {\frac{{{s_{m}^{H}{\overset{\sim}{R}}_{c}^{- 1}z_{{UTD},k_{u}}}}^{2}}{\left( {s_{m}^{H}{\overset{\sim}{R}}_{c}^{- 1}s_{m}} \right)\left( {z_{{UTD},k_{u}}^{H}{\overset{\sim}{R}}_{c}^{- 1}z_{{UTD},k_{u}}} \right)}.}$wherein H denotes the Hermitian matrix, and Z_(UTD,k) _(u) , s_(m) and{tilde over (R)}_(c) are defined as above.
 19. A method according toclaim 18 wherein said M-length threshold vector, γ, is computed usingthe equation: $\gamma = {\begin{bmatrix}{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {1,k_{u}} \right)}}} \\M \\{\frac{1}{K_{u}}{\sum\limits_{k_{u} = 1}^{K_{u}}{{ACE}_{UTD}\left( {M,k_{u}} \right)}}}\end{bmatrix}.}$
 20. A method according to claim 19 wherein thequiescent adaptive coherence estimate threshold level is scaled toobtain a desired level of false alarms.
 21. A method according to claim20 wherein the threshold is scaled using a minimum desired thresholdlevel.
 22. A method according to claim 21 wherein the scaled threshold,denoted τ_(m), for the m^(th) Doppler band is scaled asτ_(m)=max(βγ_(m),τ_(min)) wherein β is a scale factor used to set adesired probability of false alarm which is constant over m=1, 2, . . ., M, γ_(m) is the value of the threshold for the m^(th) Doppler, andτ_(min) is a minimum desired threshold level.